- Quantum chemistry
Quantum chemistry is a branch of
theoretical chemistry, which applies quantum mechanicsand quantum field theoryto address issues and problems in chemistry. The description of the electronic behavior of atoms and molecules as pertaining to their reactivityis one of the applications of quantum chemistry. Quantum chemistry lies on the border between chemistryand physics, and significant contributions have been made by scientists from both fields. It has a strong and active overlap with the field of atomic physicsand molecular physics, as well as physical chemistry.Quantum chemistry is that branch of physical chemistry,which applies quantum mechanics and field theory to understand electronic behaviour of atoms and molecules,and their reactivity.
Quantum chemistry mathematically describes the fundamental behavior of
matterat the molecular scale. [cite web | title = Quantum Chemistry | url = http://cmm.cit.nih.gov/modeling/guide_documents/quantum_mechanics_document.html | publisher = National Institutes of Health| work = The NIH Guide to Molecular Modeling | accessdate = 2007-09-08] It is, in principle, possible to describe all chemical systems using this theory. In practice, only the simplest chemical systems may realistically be investigated in purely quantum mechanical terms, and approximations must be made for most practical purposes (e.g., Hartree-Fock, post Hartree-Fockor Density functional theory, see computational chemistryfor more details). Hence a detailed understanding of quantum mechanicsis not necessary for most chemistry, as the important implications of the theory (principally the orbital approximation) can be understood and applied in simpler terms.
In quantum mechanics (several applications in computational chemistry and quantum chemistry), the Hamiltonian, or the physical state, of a particle can be expressed as the sum of two operators, one corresponding to
kinetic energyand the other to potential energy. The Hamiltonianin the Schrödinger wave equationused in quantum chemistry does not contain terms for the spin of the electron.
Solutions of the Schrödinger equation for the hydrogen atom gives the form of the wave function for
atomic orbitals, and the relative energy of the various orbitals. The orbital approximation can be used to understand the other atoms e.g. helium, lithiumand carbon.
The history of quantum chemistry essentially began with the 1838 discovery of
cathode raysby Michael Faraday, the 1859 statement of the black body radiationproblem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmannthat the energy states of a physical system could be discrete, and the 1900 quantum hypothesis by Max Planckthat any energy radiating atomic system can theoretically be divided into a number of discrete energy elements "ε" such that each of these energy elements is proportional to the frequency"ν" with which they each individually radiate energy, as defined by the following formula: :
where "h" is a numerical value called
Planck’s Constant. Then, in 1905, to explain the photoelectric effect(1839), i.e., that shining light on certain materials can function to eject electrons from the material, Albert Einsteinpostulated, based on Planck’s quantum hypothesis, that lightitself consists of individual quantum particles, which later came to be called photons(1926). In the years to follow, this theoretical basis slowly began to be applied to chemical structure, reactivity, and bonding.
The first step in solving a quantum chemical problem is usually solving the
Schrödinger equation(or Dirac equationin relativistic quantum chemistry) with the electronic molecular Hamiltonian. This is called determining the electronic structure of the molecule. It can be said that the electronic structure of a molecule or crystal implies essentially its chemical properties.
The foundation of quantum mechanics and quantum chemistry is the wave model, in which the atom is a small, dense, positively charged nucleus surrounded by electrons. Unlike the earlier
Bohr modelof the atom, however, the wave model describes electrons as "clouds" moving in orbitals, and their positions are represented by probability distributions rather than discrete points. The strength of this model lies in its predictive power. Specifically, it predicts the pattern of chemically similar elements found in the periodic table. The wave model is so named because electrons exhibit properties (such as interference) traditionally associated with waves. See wave-particle duality.
:main|Valence bond theory
Although the mathematical basis of quantum chemistry had been laid by Schrödinger in 1926, it is generally accepted that the first true calculation in quantum chemistry was that of the German physicists
Walter Heitlerand Fritz Londonon the hydrogen (H2) molecule in 1927. Heitler and London's method was extended by the American theoretical physicist John C. Slaterand the American theoretical chemist Linus Paulingto become the Valence-Bond (VB) [or Heitler-London-Slater-Pauling (HLSP)] method. In this method, attention is primarily devoted to the pairwise interactions between atoms, and this method therefore correlates closely with classical chemists' drawings of bonds.
:main|Molecular orbital theory
An alternative approach was developed in 1929 by
Friedrich Hundand Robert S. Mulliken, in which electrons are described by mathematical functions delocalized over an entire molecule. The Hund-Mulliken approach or molecular orbital (MO) method is less intuitive to chemists, but has turned out capable of predicting spectroscopic properties better than the VB method. This approach is the conceptional basis of the Hartree-Fockmethod and further post Hartree-Fockmethods.
Density functional theory
:main|Density functional theory
The Thomas-Fermi model was developed independently by Thomas and Fermi in 1927. This was the first attempt to describe many-electron systems on the basis of
electronic densityinstead of wave functions, although it was not very successful in the treatment of entire molecules. The method did provide the basis for what is now known as density functional theory. Though this method is less developed than post Hartree-Fock methods, its lower computational requirements allow it to tackle larger polyatomic molecules and even macromolecules, which has made it the most used method in computational chemistryat present.
A further step can consist of solving the
Schrödinger equationwith the total molecular Hamiltonianin order to study the motion of molecules. Direct solution of the Schrödinger equation is called "quantum molecular dynamics", within the semiclassicalapproximation "semiclassical molecular dynamics", and within the classical mechanicsframework " molecular dynamics(MD)". Statistical approaches, using for example Monte Carlo methods, are also possible.
Adiabatic chemical dynamics
:"Main article: Adiabatic formalism or Born-Oppenheimer approximation"In adiabatic dynamics, interatomic interactions are represented by single scalar
potentials called potential energy surfaces. This is the Born-Oppenheimer approximationintroduced by Born and Oppenheimer in 1927. Pioneering applications of this in chemistry were performed by Rice and Ramsperger in 1927 and Kassel in 1928, and generalized into the RRKMtheory in 1952 by Marcus who took the transition statetheory developed by Eyring in 1935 into account. These methods enable simple estimates of unimolecular reaction ratesfrom a few characteristics of the potential surface.
Non-adiabatic chemical dynamics
Non-adiabatic dynamics consists of taking the interaction between several coupled potential energy surface (corresponding to different electronic
quantum states of the molecule). The coupling terms are called vibronic couplings. The pioneering work in this field was done by Stueckelberg, Landau, and Zener in the 1930s, in their work on what is now known as the Landau-Zener transition. Their formula allows the transition probability between two diabaticpotential curves in the neighborhood of an avoided crossingto be calculated.
Quantum chemistry and quantum field theory
The application of
quantum field theory(QFT) to chemical systems and theories has become increasingly common in the modern physical sciences. One of the first and most fundamentally explicit appearances of this is seen in the theory of the photomagneton. In this system, plasmas, which are ubiquitous in both physics and chemistry, are studied in order to determine the basic quantization of the underlying bosonic field. However, quantum field theory is of interest in many fields of chemistry, including: nuclear chemistry, astrochemistry, sonochemistry, and quantum hydrodynamics. Field theoretic methods have also been critical in developing the ab initio Effective Hamiltonian theory of semi-empirical pi-electron methods.
Quantum chemistry computer programs
Condensed matter physics
International Academy of Quantum Molecular Science
*cite book |author=Pauling, L.|title=
General Chemistry|publisher=Dover Publications|year=1954|id= ISBN 0-486-65622-5
*Pauling, L., and Wilson, E. B. "Introduction to Quantum Mechanics with Applications to Chemistry" (Dover Publications) ISBN 0-486-64871-0
*Atkins, P.W. "Physical Chemistry" (Oxford University Press) ISBN 0-19-879285-9
* McWeeny, R. "Coulson's Valence" (Oxford Science Publications) ISBN 0-19-855144-4
*Landau, L.D. and Lifshitz, E.M. "Quantum Mechanics:Non-relativistic Theory"(Course of Theoretical Physics vol.3) (Pergamon Press)
*Eric R. Scerri, The Periodic Table: Its Story and Its Significance, Oxford University Press, 2006. Considers the extent to which chemistry and especially the periodic system has been reduced to quantum mechanics. ISBN 0-19-530573-6
* [http://vergil.chemistry.gatech.edu/notes/index.html The Sherrill Group - Notes]
* [http://www.shodor.org/chemviz/ ChemViz Curriculum Support Resources]
* [http://www.quantum-chemistry-history.com/ Early ideas in the history of quantum chemistry]
Nobel lectures by quantum chemists
* [http://nobelprize.org/chemistry/laureates/1998/kohn-lecture.html Walter Kohn's Nobel lecture]
* [http://nobelprize.org/chemistry/laureates/1992/marcus-lecture.html Rudolph Marcus' Nobel lecture]
* [http://nobelprize.org/chemistry/laureates/1966/mulliken-lecture.html Robert Mulliken's Nobel lecture]
* [http://nobelprize.org/chemistry/laureates/1954/pauling-lecture.html Linus Pauling's Nobel lecture]
* [http://nobelprize.org/chemistry/laureates/1998/pople-lecture.html John Pople's Nobel lecture]
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